Question

1. a cannonball is fired at some upward angle diagonal to the ground. during its flight, neglecting air resistance, it accelerates...

a. downward only.
b. upward and downward.
c. both vertically and horizontally.
d. horizontally only

1. a ball is thrown straight upward at 10 m/s. ideally (no air resistance), the ball will return to the thrower’s hand with a speed of

a. 0 m/s.
b. 5 m/s.
c. 10 m/s.
d. 20 m/s.
e. there is not enough information to say.

1. in the figure above, which diagram represents the vector addition c = a + b?

a. i
c. iii
b. ii
d. iv

1. an ant on a picnic table travels 30 cm eastward, then 25 cm northward, and finally 15 cm westward. what is the magnitude of the ant’s displacement relative to its original position?

a. 70 cm
c. 52 cm
b. 57 cm
d. 29 cm

1. which graph best represents the magnitude of the ball’s vertical velocity as it travels?

Explanation:

Step1: Analyze cannon - ball motion

In projectile motion, neglecting air - resistance, the only force acting on the cannonball is gravity. Gravity acts downward, so the acceleration is downward only. The horizontal component of velocity is constant (no horizontal acceleration). So for question 13, the answer is a.

Step2: Analyze ball thrown upward

Using conservation of mechanical energy, when a ball is thrown straight upward and there is no air - resistance, the initial kinetic energy $\frac{1}{2}mv_{0}^{2}$ is converted to potential energy at the maximum height and then back to kinetic energy as it falls. Since mechanical energy is conserved, the speed of the ball when it returns to the thrower's hand is the same as the initial speed. So for question 14, the answer is c.

Step3: Analyze vector addition

In vector addition $\mathbf{C}=\mathbf{A}+\mathbf{B}$, we place the tail of $\mathbf{B}$ at the head of $\mathbf{A}$, and the vector $\mathbf{C}$ goes from the tail of $\mathbf{A}$ to the head of $\mathbf{B}$. Diagram I represents this correctly. So for question 15, the answer is a.

Step4: Calculate ant's displacement

The ant moves 30 cm eastward and 15 cm westward, so the net east - west displacement is $x = 30 - 15=15$ cm eastward. It moves 25 cm northward. Using the Pythagorean theorem $d=\sqrt{x^{2}+y^{2}}$, where $x = 15$ cm and $y = 25$ cm. $d=\sqrt{15^{2}+25^{2}}=\sqrt{225 + 625}=\sqrt{850}\approx29$ cm. So for question 16, the answer is d.

Step5: Analyze ball's vertical velocity

When the ball is thrown upward, its vertical velocity decreases (due to gravity) until it reaches the maximum height where the vertical velocity is 0. Then as it falls, the vertical velocity increases in the downward direction. The magnitude of the vertical velocity first decreases to 0 and then increases. Graph A represents this correctly.

Answer:

1. a. Downward only.
2. c. 10 m/s.
3. a. I
4. d. 29 cm
5. A